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QUESTION: 1

Solution:

QUESTION: 2

Break : Piece

Solution:

QUESTION: 3

Replace the phrase printed in bold to make it grammatically correct ?

__ "Even though many companies"__ are now penetrating rural India, it would help to give India a real chance of witnessing a double digit GDP growth.

Solution:

QUESTION: 4

Improve the sentence with suitable options by replacing the underlined word.

He is still in vigorous health although he is on the "__right"__ side of sixty.

Solution:

QUESTION: 5

Complete the given sentence by choosing the correct phrase.

You cannot succeed unless

You cannot succeed unless

Solution:

QUESTION: 6

Chirag decided to give 12% of his salary to his younger brother as a pocket money. But he gave 1260 Rs which was 60% of what he had decided earlier. How much is Chiragâ€™s salary?

Solution:
Let x be Chiragâ€™s salary:

x = 17500 Rs

x = 17500 Rs

QUESTION: 7

Two pipes can fill a tank in 15 minutes and 25 minutes respectively. Both the pipes are opened together and after some time, the first pipe is closed and the tank is completely full in 15 minutes. For how many minutes is the first pipe opened?

Solution:

t = 6 min.

t = 6 min.

QUESTION: 8

A and B are required to solve a problem independently. If 1/2 and 1/3 are their respectively probabilities of solving the problem, then the probability that atleast one of them solves the problem.

Solution:
Probability that atleast one of them solves the problem = P

QUESTION: 9

What is the probability that a leap year has 53 Sundays and 52 Mondays?

Solution:
In leap year there are 366 days.

There are 52 weeks + 2 days

1. - Mon. + Tue.

2. - Tue. + Wed.

3. - Wed. + Thu.

4. - Thu. + Fri.

5. - Fri. + Sat.

6. - Sat. + Sun. = 53 Sundays + 52 Mondays

7. - Sun. + Mon.

Probability =1/7

There are 52 weeks + 2 days

1. - Mon. + Tue.

2. - Tue. + Wed.

3. - Wed. + Thu.

4. - Thu. + Fri.

5. - Fri. + Sat.

6. - Sat. + Sun. = 53 Sundays + 52 Mondays

7. - Sun. + Mon.

Probability =1/7

QUESTION: 10

A certain sum of money is invested for one year at a certain rate of simple interest. If the rate of interest is 3% higher, then the interest earned will be 25% more than the interest earned earlier. What is the earlier rate of interest ?

Solution:

r = 12% per annum

r = 12% per annum

QUESTION: 11

The circuit shown below is driven by a sinusoidal input The steady state output is

Solution:

QUESTION: 12

Determine the value of load resistance ,so that it receive maximum power from the circuit.

Solution:

QUESTION: 13

A plant has the following transfer function, For an unit step input determine the time required so that response will settle in 2% of its final value.

Solution:

QUESTION: 14

The open loop transfer function of an unity feedback control system is G(S) = What is the range of K so that closed loop system becomes stable ?

Solution:
Characteristics equation

= K + S(S+1) (S + 5) = 0

Rough-array

So for stable system K > 0 and

30 â€“ k > 0

k < 30

so 0 < k < 30

= K + S(S+1) (S + 5) = 0

Rough-array

So for stable system K > 0 and

30 â€“ k > 0

k < 30

so 0 < k < 30

QUESTION: 15

Determine the peak inverse voltage that appear across the diode in the given circuit.

Solution:

During positive half cycle capacitor get charge and during negative half cycle the equivalent circuit is shown as

During positive half cycle capacitor get charge and during negative half cycle the equivalent circuit is shown as

QUESTION: 16

Determine the power dissipated across the load resistance RL in the given circuit, assume diode is ideal.

Solution:

= 125 mw

= 125 mw

QUESTION: 17

What is the load current in the circuit shown below:

Solution:

= â€“ 10mA

= â€“ 10mA

QUESTION: 18

How many standard resistor are required to design a 3 bit flash type ADC?

Solution:

= 8

= 8

QUESTION: 19

Determine the size of ROM required to implement a full-substractor.

Solution:
For full-substractor, the number of input variable is 3 and output function are 2 So size of ROM,

QUESTION: 20

Determine the even part of the signal x(f) where x(t) = 4 Sin t

Solution:
x(t) = 4 sint

Since the above signal is an odd signal therefore, its even part is zero.

Since the above signal is an odd signal therefore, its even part is zero.

QUESTION: 21

An LTI system is characterized by difference equation y (n) = y (n-1) + x (n). The impulse response of the system is :

Solution:
y(n) = y(n â€“ 1) + x(n)

QUESTION: 22

Consider the signal Let denotes the Fourier transform of the signal, the value of is

Solution:

QUESTION: 23

In the given circuit, the forward threshold voltage of the diode is 0.7 and maximum power dissipation across the diode is 21mW. Determine the value of resistance R for safe operation.

Solution:

QUESTION: 24

When a bypass capacitor is connected across the emitter and resistance of a common-emitter BJT amplifier:

Solution:

QUESTION: 25

An amplifier using an op-amp with a slew rate 1 has a gain of 20 dB. If the peak value of sinusoidal input signal is 1 V then determine the maximum frequency of the input signal that can be amplify without any distortion.

Solution:
For distortion less output,

QUESTION: 26

The skin depth of copper at a frequency of 6GHz is 1the skin depth at a frequency of 24 GHz would be :

Solution:

QUESTION: 27

An air filled rectangular waveguide with dimension where b < a < 2b is to be constructed to operate at 3GHz in dominant mode. The design frequency is at least 20% higher than the cut-off frequency of dominant mode and also at least 20% below, cut off frequency of next higher mode, determine the phase velocity.

Solution:

QUESTION: 28

For FM broadcasting, the frequency deviation is 15 KHz, determine the percentage modulation of the signal.

Solution:

= 15/75 = 20%

= 15/75 = 20%

QUESTION: 29

Auto correlation function of a random signal with zero mean is given as The rms value of the AC component of the signal will be

Solution:

QUESTION: 30

An angle modulated signal is given as, considering s(t) is an FM signal and message signal m(t) is 10 then determine the value of

Solution:

QUESTION: 31

The value of dx is equal to

Solution:

QUESTION: 32

Evaluate where C represents a circle Z - 4 = 2,

Solution:

QUESTION: 33

From his 9 friends (4 boys and 5 girls), Mohan wanted to invite friends for picnic. If there have to be exactly 3 girls in invites, then the number of ways in which he can invite them are,

Solution:
Three girls can be selected from 5 girls in ways. As number of boys to be invited is not given, hence out of 4 boys he can invite them in ways, so total of

QUESTION: 34

A dice is rolled 5 times. The probability that 4 will show up exactly 3 times is:

Solution:
Probability of getting four is,

QUESTION: 35

Consider a vector A given by : at point is (1, -1, 1) is

Solution:

= 2 â€“ 6 + 1

= â€“3

= 2 â€“ 6 + 1

= â€“3

QUESTION: 36

Determine in the given circuit below

Solution:

= â€“4 volt

= â€“4 volt

QUESTION: 37

The Y-parameter of the circuit shown below :

Solution:

QUESTION: 38

In the circuit shown below, the switch is closed at t=0, determine

Solution:

QUESTION: 39

A signal is sampled at the rate of 15 Hz and applied to ideal rectangular LPF with cut-off frequency of 10Hz, then the output of filter contains

Solution:

QUESTION: 40

The value of

Solution:

QUESTION: 41

The ROC of z transform of signal is

Solution:

Since there is no any common ROC so, z-transform does not exist.

Since there is no any common ROC so, z-transform does not exist.

QUESTION: 42

The system matrix of a continuous time system is described in the state variable form is,

The system is stable for

The system is stable for

Solution:

For stable system all the elements in the first column of Routh-array should be positive. In the given option, option (c) satisfy the criteria i.e.,

For stable system all the elements in the first column of Routh-array should be positive. In the given option, option (c) satisfy the criteria i.e.,

QUESTION: 43

The maximum permissible distance between two samples of a 10 kHz signal

Solution:

QUESTION: 44

The open-loop transfer function of unity feedback control system is The system is stable for.

Solution:
Characteristic equation K + S(S + a) (S + b) = 0

For stability K > 0

and, ab (a + b) â€“ K > 0

K < ab (a + b)

So, 0 < K < ab (a + b)

For stability K > 0

and, ab (a + b) â€“ K > 0

K < ab (a + b)

So, 0 < K < ab (a + b)

QUESTION: 45

In the given logic diagram the propagation delays of both the gates are 20 nsec each. The output y is at logic â€˜1â€™ from a long time and at t = 0, the input x change from 0 to 1, so the output goes momentary to logic 0,determine the time required by the output to again maintain its level at logic 1.

Solution:

So output again becomes 1 after 40 nsec.

So output again becomes 1 after 40 nsec.

QUESTION: 46

For the power amplifier circuit shown below, the maximum power dissipated by both output transistor is

Solution:

The maximum power dissipated by both output transistor is maximum

QUESTION: 47

In the circuit A = 1, B = 1, what will be the output and when the clock input (CK) is applied ?

Solution:

QUESTION: 48

In the given circuit, the feedback factor is :

Solution:

QUESTION: 49

The current through the resistor R in the given circuit.

Solution:

QUESTION: 50

Determine the operating point of the BJT, in the given circuit.

Solution:

= 7.85 â€“ 4.3

= 3.55 V

= 7.85 â€“ 4.3

= 3.55 V

QUESTION: 51

In the circuit shown in the given figure, assume that the capacitor C is almost shorted for the frequency range of interest of the input signal. Under this condition, the voltage gain of the amplifier will be approximately.

Solution:
It is common collector configuration (emitter follower) so voltage gain is almost equal to 1, in the given option

QUESTION: 52

For a Si transistor connected as shown in the fig = 0.7V. Given that the reverse saturation current of the junction at room temperature is 200 nA, the IC is given by

Solution:
Since base is connected to collector of the transistor, therefore it works as a diode

QUESTION: 53

The Fermi-level of a material is 3eV, then the velocity of electron at Fermi-level is :

Solution:

QUESTION: 54

Magnetic flux density in certain medium with permeability is given by . is given by,

Solution:
The current-density

QUESTION: 55

Given field, It can be said that A is

Solution:

So given field is conservative

So given field is conservative

QUESTION: 56

Two lossless lines are connected as shown in figure below. The input impedance seen across the terminal AB is

Solution:

QUESTION: 57

An angle-modulated signal is expressed by, Determine the range of maximum frequency swing

Solution:

= 2 Ã— 75

= 150 KHz

= 2 Ã— 75

= 150 KHz

QUESTION: 58

A binary source generates digits 1 and 0 randomly with equal probability. Then the probability three 1 and four 0 with respect to 7 digits generated by the source is

Solution:

= 35/128

= 35/128

QUESTION: 59

Consider the octal signal point constellation in figure shown below. The adjacent signal point in the 8-PSK are separated by a distance 1 unit. Then the radius r of the circle is

Solution:
r is the radius of circle, by cosine theorem

QUESTION: 60

Consider the audio signal with spectral components limited to the frequency band of 300 to 3300 Hz. A PCM signal is generated with a sampling rate of 8000 samples/sec. The required output signal to quantizing noise ratio is 30 dB. The minimum number of bits per sample needed is :

Solution:
(SNR) in dB = 1.76 + 20 log L

Where L is the number of levels

So minimum number of levels are 26, and minimum number of bits are 5.

Where L is the number of levels

So minimum number of levels are 26, and minimum number of bits are 5.

QUESTION: 61

X is a binary memory less source with P(x=0) = 0.3. This source is transmitted over a binary symmetric channel with crossover probability P = 0.1. Assume that the source is directly connected to the channel, i.e. no coding is employed. Then the error probability at the destination is

Solution:
Probability of error is given as

QUESTION: 62

Given a > 0, we wish to calculate the reciprocal value by Newton â€“ Raphson method for f(x)=0 for a=7 and starting with = 0.2, the first two iterations would be :

Solution:

QUESTION: 63

Consider the system of equations

ax + 3y + z = 5

2x â€“ y + 2az = 3

x + 4y + az = 6

The value of a for which the above equations posses an unique solution.

ax + 3y + z = 5

2x â€“ y + 2az = 3

x + 4y + az = 6

The value of a for which the above equations posses an unique solution.

Solution:
Determinant of matrix A,

a{â€“ a â€“8a} â€“3{2a â€“ 2a} + 1 {1 + 4}

a{â€“ a â€“8a} â€“3{2a â€“ 2a} + 1 {1 + 4}

QUESTION: 64

Cayley-Hamilton Theorem states that a square matrix satisfies its own characteristic equation. Consider a matrix A = the value of is

Solution:

QUESTION: 65

is increasing in the interval given below, choose the correct option.

Solution:

x(x â€“ 3) â€“2 (x â€“ 3) = 0

(x â€“ 3) (x â€“ 2) = 0

So, x = 2, 3

According to curve wave method for increasing function

x(x â€“ 3) â€“2 (x â€“ 3) = 0

(x â€“ 3) (x â€“ 2) = 0

So, x = 2, 3

According to curve wave method for increasing function

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